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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

In the figure above, which quadrants contain pairs (x , y) that satisfy the condition x /y = 1?

(A) I only
(B) I and II only
(C) I and III only
(D) II and IV only
(E) I, II, III, and IV

答案和解析

答案：C

解析：

In order for (x , y) to satisfy x / y = 1, it must be true that x and y are equal to each other and not equal to zero. An example of such a pair is (3 , 3), which is in quadrant I.

In quadrant II, all the x values are negative and all the yvalues are positive, so in quadrant II, x and y cannot be equal. For example, the pair (- 3 , 3) does not satisfy the condition, since (negative 3 / 3) = negative 1, not 1.

In III, the x values and the y values are both negative, so it is possible for x and y to be equal. For example, the pair (- 3 , - 3) is in III and - 3 / - 3 = 1.

In quadrant IV, x and y cannot be equal because the x values are positive and the y values are negative. For example, the pair (3 , - 3) does not satisfy the condition, since 3 / - 3 = - 1.

The quadrants that contain pairs (x , y) that satisfy the given condition are quadrants I and III only.